Negative mass would possess some strange properties, such as accelerating in the direction opposite of applied force. Despite being inconsistent with the expected behavior of "normal" matter, negative mass is mathematically consistent and introduces no violation of conservation of momentum or energy. It is used in certain speculative theories, such as on the construction of artificial wormholes and the Alcubierre drive. The closest known real representative of such exotic matter is the region of pseudo-negative-pressure density produced by the Casimir effect.

According to mass–energy equivalence, mass m{\displaystyle m} is in proportion to energy E{\displaystyle E} and the coefficient of proportionality is c2{\displaystyle c^{2}}. Actually, m{\displaystyle m} is still equivalent to E{\displaystyle E} although the coefficient is another constant[8] such as −c2{\displaystyle -c^{2}}.[9] In this case, it is unnecessary to introduce a negative energy because the mass can be negative although the energy is positive. That is to say,

If the rest mass m{\displaystyle m} is complex this implies that the denominator is complex because the total energy is observable and thus must be real. Therefore, the quantity under the square root must be negative, which can only happen if v is greater than c. As noted by Gregory Benfordet al.,special relativity implies that tachyons, if they existed, could be used to communicate backwards in time[12] (see tachyonic antitelephone). Because time travel is considered to be non-physical, tachyons are believed by physicists either not to exist, or else to be incapable of interacting with normal matter.

At high pressure, materials such as sodium chloride (NaCl) in the presence of an excess of either chlorine or sodium were transformed into compounds "forbidden" by classical chemistry, such as Na3Cl and NaCl3. Quantum mechanical calculations predict the possibility of other compounds, such as NaCl7, Na3Cl2 and Na2Cl. The materials are thermodynamically stable at high pressures. Such compounds may exist in natural environments that exist at high pressure, such as the deep ocean or inside planetary cores. The materials have potentially useful properties. For instance, Na3Cl is a two-dimensional metal, made of layers of pure sodium and salt that can conduct electricity. The salt layers act as insulators while the sodium layers act as conductors.[13][14]

Antimatter – Material composed of the antiparticles of the corresponding particles of ordinary matter

Dark energy – An unknown physical entity (lato sensu) that causes the expansion of the universe to accelerate. It might be a completely new component of physics or a broader extension of known physics, for example, gravity.

Dark matter – Hypothetical form of matter comprising most of the matter in the universe